In order to illustrate the typical size of resummation effects, we solve the RG evolution equations numerically for two representative examples: the decays \(Z^{\prime }\rightarrow t\bar{t}\)  and \(Z^{\prime }\rightarrow W^+ W^-\) , both evaluated at leading order in the expansion in powers of \(\lambda \)  and for a mass \(m_{Z^{\prime }}=3\)  TeV of the new \(Z^{\prime }\)  boson. A consistent solution at leading order in RG-improved perturbation theory requires that one uses the two-loop expressions for the cusp anomalous dimensions in (REF ) and for the \(\beta \) -functions of the SM gauge couplings [1]}, while the one-loop expressions are sufficient for all other anomalous dimensions
and for the \(\beta \) -function of the top-quark Yukawa coupling. The latter one is given by [2]}
\(\mu \,\frac{d}{d\mu }\,y_t = \frac{9{\hspace{0.85358pt}}y_t^3}{32\pi ^2}- y_t \left( \frac{17\alpha _1}{48\pi } + \frac{9\alpha _2}{16\pi } + \frac{2\alpha _3}{\pi } \right) .\) 
